Critical Particle Volume Fraction Research Articles

Rheology of a nematic active suspension undergoing oscillatory shear and step strain flows

We investigate experimentally the rheology of an active suspension of nematodes C. elegans under oscillatory shear. There are few experimental investigations and theoretical work on the oscillatory rheological properties including elastic and viscous moduli of micro-swimmer suspensions. The viscous and elastic moduli are evaluated by our experiments in the regime of linear viscoelasticity. These viscoelastic quantities are explored at low frequency given the active suspension viscosity and the shear elastic modulus. The experiments have revealed an anomalous behavior of the viscosity and the shear elastic modulus with the variation of the suspension volume fraction. The suspension relative viscosity decreased with the increase of active particles within a certain range of volume fraction. However, above a critical particle volume fraction, the relative viscosity increases. This observed increase of the viscosity for larger concentration is a direct consequence of formation of large and coherent oriented structures and active particle interactions. This collective behavior also increases the first normal stress difference N1, obtained through Cox–Merz rule. Three different regions are obtained regarding different involved mechanisms and a physical interpretation is provided based on the particles dipole stresslet. Step strain tests are carried out and the active relaxation time as a function of volume fractions are obtained. An intrinsic oscillatory behavior is observed regardless the volume fraction, showing the non-equilibrium condition of the active suspension.

The Origins of Enhanced and Retarded Crystallization in Nanocomposite Polymers.

Controlling the crystallinity of hybrid polymeric systems has an important impact on their properties and is essential for developing novel functional materials. The crystallization of nanocomposite polymers with gold nanoparticles is shown to be determined by free space between nanoparticles. Results of large-scale molecular dynamics simulations reveal while crystallinity is affected by the nanoparticle size and its volume fraction, their combined effects can only be measured by interparticle free space and characteristic size of the crystals. When interparticle free space becomes smaller than the characteristic extended length of the polymer molecule, nanoparticles impede the crystallization because of the confinement effects. Based on the findings from this work, equations for critical particle size or volume fraction that lead to this confinement-induced retardation of crystallization are proposed. The findings based on these equations are demonstrated to agree with the results reported in experiments for nanocomposite systems. The results of simulations also explain the origin of a two-tier crystallization regime observed in some of the hybrid polymeric systems with planar surfaces where the crystallization is initially enhanced and then retarded by the presence of nanoparticles.

Electromagnetic Properties of Fe50Co50/Cu Granular Composite Materials Containing Flaky Particles

Electromagnetic properties of Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> /Cu hybrid granular composite materials containing flaky Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> particles and flaky Cu ones have been studied in the RF to microwave frequency range to realize the double negative (DNG) material. The electrical percolation along the dispersed Cu particle chains takes place at the critical Cu particle volume fraction φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c_Cu</sub> = 0.07; the σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> value of composites with φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c_Cu</sub> and above was more than 10-1 S/cm. The negative permittivity caused by the low-frequency plasma oscillation of conduction electron in percolated Cu particle chains was observed above φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cu</sub> = 0.08; the hybrid composites with φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cu</sub> 0.08 are in the low-frequency plasmonic state. Meanwhile, the negative permeability due to the magnetic resonances was obtained above φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cu</sub> = 0.10. Therefore, in the Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> /Cu flaky particle composites with φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Cu</sub> 0.10, the DNG characteristics were realized by the low-frequency plasma oscillation and magnetic resonances in the RF to microwave frequency range. In the Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> /Cu flaky particle composites, the DNG spectrum was observed at relatively low Cu particle content and the DNG frequency band becomes broad compared to the Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> Co <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">50</sub> /Cu hybrid composites containing spherical or arborized shape particles.

A novel method for prediction of tensile strength of spherical particle-filled polymer composites with strong adhesion

By analyzing the breakage of composites from a new perspective, the tensile strength of composites filled with spherical particles is studied in this article. A large number of experimental data are summed up, and a novel form of formula that can predict the tensile strength of composites is put forward. This form of formula focuses on the composites that possess strong adhesion strength between particles and polymer matrix. High particle volume fraction results in a phenomenon that the particles in composites have a tendency to aggregate. So, the influence of the particle aggregation is also studied in this article. A critical particle volume fraction is proposed to describe that at what value of particle volume fraction the clusters begin to form. And an aggregation factor is put forward to describe the extent that the clusters diminish the composite's tensile strength. A good agreement between the results of the prediction by this article and the experimental data in many references has been found, which validates the accuracy of the theory. POLYM. ENG. SCI., 2016. © 2016 Society of Plastics Engineers

Investigation on the Mixing Stability of Asphalt Emulsion with Cement through Viscosity

AbstractCement asphalt emulsion (CA) mortar is a key material in the nonballast slab track. Its properties are largely dependent on the compatibility between asphalt emulsion and cement. The mixing stability of asphalt emulsion with cement is investigated by analyzing the viscosity of CA paste. Viscosity and the critical particle volume fraction of CA paste are proposed as indexes in evaluating the mixing stability of asphalt emulsion with cement, and factors influencing the mixing stability of asphalt emulsion are studied. Mixing stability is dependent on mixing method, superplasticizer, and emulsion type. The premixing cement method, superplasticizer, and good asphalt emulsion can increase the critical particle volume fraction of CA paste, which is helpful in achieving a low water–to–cement mass ratio (W/C). Anionic emulsion has much better mixing stability with cement than does cationic emulsion. The critical particle volume fraction of CA pastes with anionic emulsion increases stably with the mass rat...

Study of the effect of particle volume fraction on the microstructure of magnetorheological fluids using ultrasound: Transition between the strong-link to the weak-link regimes

The effect of particle volume fraction on the microstructure of magnetorheological (MR) fluids has been studied using ultrasonic techniques. When no magnetic field is applied, they behave as slurry. However, when magnetic field is applied, important features regarding the change of the microstructure have been found with the help of ultrasonic waves propagating in the direction of the magnetic field. As the volume fraction increases, a rearrangement of particles which decrease the compressibility of the system is detected; nevertheless, the material behaves as a non-consolidated material. Three different particle volume fraction regions are found identifying a critical particle volume fraction predicted in the literature. Ultrasounds are confirmed as an interesting tool to study MR fluids in static conditions.

Towards a generic method for inorganic porous hollow fibers preparation with shrinkage-controlled small radial dimensions, applied to Al2O3, Ni, SiC, stainless steel, and YSZ

A versatile method is presented for the preparation of porous inorganic hollow fibers with small tunable radial dimensions, down to ∼250 μm outer diameter. The approach allows fabrication of thin hollow fibers of various materials, as is demonstrated for alumina, nickel, silicon carbide, stainless steel, and yttria stabilized zirconia. The preparation method is based on dry-wet spinning of a particle-loaded polymer solution followed by thermal treatment. Exceptionally small radial dimensions have been achieved by surface energy driven viscous flow of the green fiber, resulting in a reduction of macro-void volume. It is shown that the extent of viscous deformation is directly related to the rheology of the particle-loaded green fiber above the glass transition temperature of the polymer. A particle specific limited concentration range can be identified in which viscous deformation is possible. Above a critical particle volume fraction the viscosity of the particle–polymer material increases sharply and the time scale of viscous deformation becomes too long. Below a minimum concentration of particles it is not possible to sinter the particles together. For small particles of alumina, silicon carbide, and yttria stabilized zirconia the concentration range allowing viscous deformation is very narrow as compared to that of larger metal particles.

Polymer nanocomposites: polymer and particle dynamics

Polymer nanocomposites containing nanoparticles smaller than the random coil size of their host polymer chains are known to exhibit unique properties, such as lower viscosity and glass transition temperature relative to the neat polymer melt. It has been hypothesized that these unusual properties result from fast diffusion of the nanostructures in the host polymer, which facilitates polymer chain relaxation by constraint release and other processes. In this study, the effects of addition of sterically stabilized inorganic nanoparticles to entangled cis-1,4-polyisoprene and polydimethylsiloxane on the overall rheology of nanocomposites are discussed. In addition, insights about the relaxation of the host polymer chains and transport properties of nanoparticles in entangled polymer nanocomposites are presented. The nanoparticles are found to act as effective plasticizers for their entangled linear hosts, and below a critical, chemistry and molecular-weight dependent particle volume fraction, lead to reduced viscosity, glass transition temperature, number of entanglements, and polymer relaxation time. We also find that the particle motions in the polymer host are hyperdiffusive and at the nanoparticle length scale, the polymer host acts like a simple, ideal fluid and the composites' viscosity rises with increasing particle concentration.

Criticality for shear-induced gelation of charge-stabilized colloids

Colloidal systems that are well stabilized by electrostatic repulsive forces can be activated by intense shear flow and transformed into solid-like gels, without adding any electrolyte. We have experimentally quantified the critical particle volume fraction for such a transition and found that it is a function of primary particle radius and shear rate. In particular, the values of the critical particle volume fraction obtained under different conditions can be represented through a single power-law function of the Breakage Number (Br), which is defined as the ratio between the shearing energy and the interparticle bonding energy. This finding indicates that, instead of shear rate or stress, the correct parameter quantifying the criticality for shear-induced gelation is Br. In addition, it is shown that the clusters formed in the shear aggregation process exhibit fractal scaling with fractal dimension equal to 2.4 ± 0.04, independent of Br (i.e., of the shear stress, the particle size and the interparticle bonding energy). This is similar to the case of quiescent systems where the Brownian motion-induced aggregations, i.e., diffusion-limited and reaction-limited cluster aggregations, lead to clusters with fractal dimension equal to 1.8 ± 0.05 and 2.1 ± 0.05, respectively, which are independent of the particle type and size and the electrolyte concentration. Moreover, the ratio between the radius of gyration of clusters constructing the gel network and the primary particle radius at criticality decreases as Br increases, following a power-law scaling with exponent of −0.31, which is in good agreement with that for breakup of dense fractal clusters of the same fractal dimension in laminar flow.

Effect of Temperature on High Shear-Induced Gelation of Charge-Stabilized Colloids without Adding Electrolytes

We demonstrated previously (Wu, H.; Zaccone, A.; Tsoutsoura, A.; Lattuada, M.; Morbidelli, M. Langmuir 2009, 25, 4715) that, for a colloid stabilized by charges from both polymer chain-end groups and adsorbed sulfonate surfactants, when the surfactant surface density reaches a certain critical value, the shear-induced gelation becomes unachievable at room temperature, even at an extremely large Peclet number, Pe = 4.6 x 10(4). This is due to the presence of the short-range, repulsive hydration force generated by the adsorbed surfactant. In this work, we investigate how such hydration force affects the shear-induced gelation at higher temperatures, in the range between 303 and 338 K. It is found that a colloidal system, which does not gel at room temperature in a microchannel at a fixed Pe = 3.7 x 10(4), does gel when temperature increases to a certain value. The critical initial particle volume fraction for the gelation to occur decreases as temperature increases. These results indicate that the effect of the hydration force on the gelation decreases as temperature increases. Moreover, we have observed that at the criticality only part of the primary particles is converted to the gel network and the effective particle volume fraction forming the gel network does not change significantly with temperature. The effective particle volume fraction is also independent of the surfactant surface coverage. Since the effective particle volume fraction corresponds to space filling requirement of a standing gel network, which is mainly related to the clusters structure, this result indicates that at a given shear rate the cluster structure does not change significantly with the surfactant surface coverage. On the other hand, since the cluster morphology is a strong function of the shear rate, we have observed that when the Peclet number is lowered from Pe = 3.7 x 10(4) to 1.7 x 10(4), the effective particle volume fraction reduces from 0.19 to 0.12 at 313 K.

Cracking in Soft−Hard Latex Blends: Theory and Experiments

Volatile organic compounds (VOCs) in the traditional paint and coating formulations are an important health and environmental concern, and current formulations are increasingly moving toward water-based dispersions. However, even within the water-based systems, small quantities of organic solvents are used to promote particle coalescence. One route to achieving this goal has been to use mixtures of soft and hard particles, also known as latex blends. We investigate the drying of colloidal films containing mixtures of silica and acrylic particles. Since both the particles deform only slightly at room temperature, this work investigates the cracking behavior of films containing elastic particles of two different elastic moduli. We extend an existing model for the stress versus strain relation for identical particles in a colloidal film to that containing a mixture of equal-sized hard and soft elastic spheres while accounting for the nonaffine deformation. A transition from soft to rigidlike behavior is observed beyond a critical hard particle volume fraction ratio that matches with published results obtained from computer simulations. The model predictions are validated with extensive experimental data on the critical stress and critical cracking thickness for various ratios of hard and soft particle volume fraction.

Dynamics of Stress Bearing Particle Networks in Poly(propylene)/Alumina Nanohybrids

AbstractIn this work, we report about the relationships between the linear rheology and the microstructure of a polymer‐nanoparticle model system (i‐PP/Al2O3 nanospheres). Over a critical particle volume fraction, rheological evolutions during a quasi‐quiescent thermal annealing indicate the formation of a whole‐space‐spanning transient network of Al2O3 nanospheres, as confirmed by transmission electron microscopy. The dynamics of this network, responsible for the liquid‐like to solid‐like transition of the nanohybrid, have been investigated by means of rheological measurements. Once the network had formed, the application of large amplitude oscillatory shear progressively and irreversibly destroyed it, leading to a flow‐induced structure unable to contribute to the elasticity of the nanohybrid. Conversely, if the large deformation is applied to an unstructured sample, a solid‐like feature still emerges by ageing the sample. The resulting strength of such a nanohybrid, however, was lower than that obtainable without the application of large deformations. Energetic considerations may explain the transient nanoparticle network dynamics, strictly related to the bulk rheological properties.magnified image

Thermal stresses and related phenomena in composite ceramics

The paper deals with elastic thermal stresses in an isotropic multi-particle-matrix system consisted of periodically distributed spherical particles in an infinite matrix, imaginarily divided into cubic cells containing a central spherical particle. Originating during a cooling process as a consequence of the difference in thermal expansion coefficients between the matrix and the particle, and investigated within the cubic cell, the thermal stresses, as functions of the particle volume fraction v, being transformed for v = 0 to those of an isotropic one-particle-matrix system, are maximal at the critical particle volume fraction, representing a considerable value related to maximal resistance of the thermal-stress strengthened multi-particle-matrix system against mechanical loading. The thermal stresses are derived for such temperature range within which the multi-particle-matrix system exhibits elastic deformations, considering the yield stress and the particle-matrix boundary adhesion strength. With regard to a curve integral of the thermal-stress induced elastic energy density, critical particle radii related to crack initiation in ideal-brittle particle and matrix, functions describing crack shapes in a plane perpendicular to the direction of crack formation in the particle and in the matrix, and consequently dimensions of a crack in the particle and in the matrix are derived along with the condition concerning the direction of the crack formation. Additionally, derived by two equivalent mathematical techniques, the elastic energy gradient within the cubic cell, representing a surface integral of the thermal-stress induced elastic energy density, is presented to derive the thermal-stress induced strengthening in the spherical particle and in the cubic cell matrix. The former parameters for v = 0 are derived using the model of a spherical cell with the radius \({R_c\rightarrow\infty}\). Derived formulae are applied to the SiC–Si3N4 multi-particle-matrix system, and calculated values of investigated parameters are in a good agreement with those from published experimental results.

Thermal Stresses in SiC-Si&lt;sub&gt;3&lt;/sub&gt;N&lt;sub&gt;4&lt;/sub&gt; Cubic-Cell-Divided Multi-Particle-Matrix System

The paper deals with crack formation of thermal stresses in an isotropic multi-particle-matrix system of homogeneously distributed spherical particles in an infinite matrix divided to cubic cells containing a central particle. Originating during a cooling process as a consequence of the difference in thermal expansion coefficients between a matrix and a particle, the thermal stresses are thus investigated within the cubic cell and extreme at the critical particle volume fraction. Resulting from the derived crack formation condition related to an ideal-brittle particle, the critical particle radius considering the critical particle volume fraction is presented along with an application to the thermalstress- strengthened SiC-Si3N4 ceramics.

Effect of particle morphology and microstructure on strength, work-hardening and ductility behaviour of ODS-(7–13)Cr steels

The effect of particle morphology and grain refinement to the nanometer scale on strength, work-hardening and tensile ductility of reduced activation ODS-(7–13)Cr steels has been modelled with a dependence on deformation temperature ( T=RT–700 °C) and a superimposed irradiation hardening. The Orowan model predictions describe as the upper limit the observed particle strengthening of various ODS-(7–13)Cr-(⩽0.5 wt% yttria) steels. An optimum particle size d p ∗≅7–22 nm ( f v=0.004–0.05) and strength, together with a lower limiting ultra-fine grain size d K,c⩾90 nm result in maximum uniform ductility increase by grain refinement and dispersion hardening (DIGD). Optimum size d p ∗ increases with increasing particle volume fraction f v and deformation temperature and decreases with irradiation hardening and grain refinement. The region of DIGD is limited to achieve a critical strength σ L corresponding to a critical particle volume fraction f v,c and grain size d K,c, above which uniform strain becomes limited by the strong drop of fracture strain. Grain refinement and irradiation hardening decrease σ L, f v,c and increase d K,c. In accordance with experimental results of ODS-Eurofer, nominal uniform strain increases with increasing f v by about ε u,n= B e+ A eln f v, most strongly around 300 °C, but weakly at the 600 °C minimum. The strong ductility increase above 600 °C results from a reduction of dislocation annihilation and structural recovery of strength. At T<300 °C, grain refinement increases uniform ductility up to d K,c for lower f v toward a saturation value which increases with increasing ratio of shear modulus to Hall–Petch constant. The enhanced uniform ductility at T⩾300 °C is otherwise strongly decreased by grain refinement, more pronounced at lower f v and for strengths above σ L.

Stability of uniform fluidization revisited

The marginal stability of uniform gas-fluidized beds is analyzed making use of ‘macroscopic’ conservation equations based on a recent version of the theory of random particulate motion in dense, collisional suspensions. This version of the theory, developed by Buyevich and Kapbasov, combines the standard correlation theory of stationary random processes, applied to stochastic equations for fluctuations of the flow properties, and the generalization, to dense suspensions, of the classical Smoluchowski's theory of fluctuations of the particle concentration. It is shown that, within the framework of the adopted approach, the stability of uniform fluidization can be explained without reference to the hypothetical solid-like state of the particulate phase. The criterion of stability is derived in the form of the critical particle volume fraction as a function of the non-dimensional parameter controlling the dissipation, on interparticle collisions, of the kinetic energy of particle velocity fluctuations. The wavenumbers of ‘macroscopic’ perturbations with the maximum growth rate in the unstable fluidized bed are analyzed. Such perturbations are usually associated with the initial sizes of emerging bubbles; these sizes are obtained as functions of the particle concentration and the above mentioned parameter of inelasticity of interparticle collisions. Recent theoretical studies led to the conclusion that the apparent stability of uniform fluidization cannot be explained without taking into account yield stress caused by direct interparticle contacts. The approach of this paper provides an explanation of the stability without invoking non-hydrodynamic phenomena (except for interparticle collisions).

Effect of morphology on the brittle ductile transition of polymer blends: 5. The role of CaCO 3 particle size distribution in high density polyethylene/CaCO 3 composites

The effect of particle size distribution on the brittle ductile transition of high density polyethylene (HDPE)/CaCO 3 composites is studied. Fu and coworkers reported that the brittle ductile transition curves of HDPE/CaCO 3 composites obtained by plotting impact strength against matrix ligament thickness do not give a master curve. In this work, the splitting of brittle ductile transition master curve of the composites as matrix ligament thickness is smaller than its critical value at brittle ductile transition is demonstrated to be attributable to the effect of CaCO 3 particle size distribution on matrix ligament thickness. The critical matrix ligament thickness criterion proposed by Wu is thus valid for the brittle ductile transition of HDPE/CaCO 3 composites when the effect of particle size distribution on matrix ligament thickness is considered. The relations of critical particle size and of critical particle volume fraction at brittle ductile transition to particle size distribution are analyzed, respectively. A narrow particle size distribution is favourable to the enhancement of the toughness of polymer composites.

Shear thinning and thickening rheology: II. Volume fraction and size of dispersed particles

The empirical equation for viscosity as a function of shear rate contains a hyperbolic cosine function and predicts infinite viscosity at either zero or infinite shear rate, with a minimum viscosity at an intermediate shear rate. It contains three parameters; each is a constant multiplied by a positive or negative power of the free volume fraction. This is defined as the difference between the critical particle volume fraction for random close-packing and the actual volume fraction augmented by the volume of a stabilizing layer around each particle. The equations are applied to data for acrylic dispersions in hydrocarbon. The critical volume fraction increases as the particle radius decreases because the particles are slightly deformable; the stabilizing layer thickness agrees with a literature value (6 nm) from a different method. Of the remaining three constants, the viscosity constant is independent of radius, showing it is determined by hydrodynamics; the time constant is proportional to the fifth power of the radius, probably reflecting Brownian motion; and the dimensionless constant, which is inversely proportional to the radius squared, is possibly associated with steric interaction forces. The reduction in viscosity caused by blending different particle sizes is described, by adding an excess term to the free volume fraction and then applying the empirical equations with an average particle radius intermediate between the number and weight averages. Discontinuous or abrupt shear thickening occurs, in very concentrated dispersions, when the shear rate is raised to a value roughly proportional to the sixth power of the free volume fraction; it may be associated with particle deformability and the rate of acceleration of the motion.